In this article, I am going to explain how we can implement the AND gate using NAND gate only. In digital electronics, the AND gate is a basic logic gate, while the NAND gate is a universal logic gate. Since the NAND gate is a universal gate, it can be used to implement any kind of Boolean function without the need for other types of logic gates. Hence, we can use NAND gates to create a circuit that can produce a Boolean function equivalent to the AND gate. Before discussing the implementation of the AND gate with NAND gates, let us first get a brief overview of both the AND gate and the NAND gate individually.
What is AND Gate?
The AND gate is a basic logic gate that can have two or more inputs and one output. The output of the AND gate is logic 1 or high, if and only if all inputs are logic 1 or high. For all other input combinations, the output of the AND gate is logic 0 or low.
The operation of a two-input AND gate is given in the form of a truth table below.
|
Inputs |
Output |
|
|
A |
B |
Y |
|
0 |
0 |
0 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
The relationship between inputs and output of the AND gate is given by its Boolean expression, which is given below.
Y = A.B
Here, A and B are inputs and Y is the output.
What is NAND Gate?
The NAND gate is a universal logic gate. It can have two or more inputs and one output. The output of the NAND gate is logic 0 or low, if and only if all inputs are logic 1 or high. For all other input combinations, the output is logic 1 or higher.
The operation of a two-input NAND gate is given in the truth table below.
|
Inputs |
Output |
|
|
A |
B |
Y |
|
0 |
0 |
1 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
The relationship between inputs and output of the NAND gate is expressed by its Boolean function that is given below.
$$Y=\overline{AB}$$
Here, A and B are the inputs and Y is the output.
Now, let us understand how to implement the AND gate using NAND gates.
Implement AND Gate using NAND Gate
To implement the AND gate using NAND gates only, we first have to derive the logic function of the output of the AND gate in terms of the NAND gate. This is explained below.
The output of the AND gate is given by,
Y = AB
Using the double complement rule, we can write,
$$Y=\overline{\overline{AB}}$$
This logic function is equivalent to the output of the AND gate. We can implement this function by using two NAND gates.
Circuit Diagram of AND Gate using NAND Gate:
The circuit diagram of the AND gate using the NAND gate is shown in the following figure.
In this circuit, the first NAND gate takes two inputs, i.e. A and B, and produces an output as per NAND gate operation. After that, the second NAND gate acts as an inverter and produces a complemented output which is equivalent to AND operation.
Conclusion
Hence, in this article, I have explained how we can implement the AND gate using NAND gates. The implementation of AND gate with NAND gates requires two NAND gates connected in series as shown in the above figure.
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